Hey!
You should add a few lines where Regulus wonders if his son is a Squib before than he gets his Hogwarts letter since he never actually saw him perform any accidental magic.
Wouldn't a Hogwarts professor come to explain magic if they believed Reggie to be a muggleborn?
I think Regulus could have sent a message to Reggie through his Patronus to prove him that magic exists.
I think Regulus could go into the Alley without being recognised if he dresses as a typical muggle. After all, he was not such a well known person before he disappeared, and everybody believes him dead, so no one would be looking for him particuliary. And you could make it so when he learns of Sirius' escape he would realize that his own brother would recognize him, even after all that time (brother bond, you know). It's up to you wether Sirius is the one to recognise him or not.
Have fun writing Reggie's and Lorraine's discovery of the wizarding world!
HpStRMlnR